NEW YORK — Donald Trump came under fire Sunday for declining to disavow the support of David Duke, the white nationalist and ex-Ku Klux Klansman who has called him “by far the best candidate.’’

Facing criticism from his rivals for the Republican presidential nomination, Trump later moved to distance himself from Duke. However, the sequence exposed Trump to questions about his judgment and fitness to be president.

“Well, just so you understand, I don’t know anything about David Duke,’’ Trump said in an interview with CNN. “I don’t know anything about what you’re even talking about with white supremacy or white supremacists.’’

Later Sunday, after a flurry of criticism about his comments, Trump responded on Twitter and retreated to the position he took when asked about Duke last week. “I disavow,’’ he wrote.

Duke has not formally endorsed Trump, but he has embraced the Republican presidential candidate’s cause wholeheartedly.

“Voting against Donald Trump at this point is really treason to your heritage,’’ Duke told his radio audience recently. Duke expanded on his support of Trump in a Facebook post over the weekend.

“I think he deserves a close look by those who believe the era of political correctness needs to come to an end,’’ Duke said, calling for a leader who would secure the border and dismantle the “Jewish controlled’’ financial industry.

The discussion of Trump’s support among white supremacists comes on a day when he also reposted a tweet quoting Benito Mussolini, the founder of the fascist movement, and called for libel laws to be weakened so that he could more easily sue the press when it covers him critically.

The campaigns of Senators Marco Rubio and Ted Cruz pounced on Trump for failing to distance himself from Duke on Sunday.

“If you need to do research on the KKK before you can repudiate them, you are not ready or fit to be president,’’ said Joe Pounder, a spokesman for Rubio.

Cruz wrote in a tweet that the situation was “sad.’’

“You’re better than this,’’ Cruz said, addressing Trump. “We should all agree, racism is wrong, KKK is abhorrent.’’

Some civil rights groups also expressed concern about a mainstream politician failing to denounce white supremacist ideology.

“Condemning David Duke and the Ku Klux Klan at every opportunity should be the easiest thing anyone can do,’’ Heidi Beirich of the Southern Poverty Law Center said. “The hatefulness of their ideas and actions are well-established and should be condemned forcefully by all responsible political leaders.’’

Trump’s lack of knowledge of Duke was surprising because he said as recently as Friday that he did disavow Duke’s support.

Trump also expressed his disapproval of Duke back in 2000 after deciding not to embark on a presidential bid in the Reform Party.

“The Reform Party now includes a Klansman, Mr. Duke, a neo-Nazi, Mr. Buchanan, and a communist, Ms. Fulani,’’ Trump said in a statement, referring to Pat Buchanan and Lenora Fulani, the former standard-bearer of the New Alliance Party and an advocate of Marxist-Leninist politics. “This is not company I wish to keep.’’

But Sunday, Trump insisted that he would not condemn someone whom he does not know anything about.

“I don’t know David Duke,’’ he said. “I don’t believe I have ever met him. I’m pretty sure I didn’t meet him. And I just don’t know anything about him.’’

Also Sunday, Trump tried to deflect attention from a class-action civil lawsuit involving the former Trump University by pointing to the ethnic background of the judge in the case.

Asked on “Fox News Sunday’’ what US District Judge Gonzalo Curiel’s ethnicity has to do with the lawsuit against him, Trump replied: ‘‘I think it has to do perhaps with the fact that I'm very, very strong on the border, very, very strong at the border, and he has been extremely hostile to me.’’

According to the California class-action complaint in front of Curiel, a one-year apprenticeship that Trump University students were promised ended after students paid for a three-day seminar. Attendees who were promised a personal photo with Trump received only the chance to take a photo with a cardboard cutout. And many instructors were bankrupt real estate investors.

Trump University emerged as a campaign issue at Thursday’s GOP debate.

“There are people who borrowed $36,000 to go to Trump University, and they’re suing now — $36,000 to go to a university that’s a fake school,’’ Rubio said. “And you know what they got? They got to take a picture with a cardboard cutout of Donald Trump.’’

Cruz jumped in, adding: “It’s a fraud case. . . . I want you to think about, if this man is the nominee, having the Republican nominee on the stand in court, being cross-examined about whether he committed fraud.’’

At a rally in Arkansas on Saturday, Trump took a break from his standard campaign speech to downplay the lawsuit pending against the business, which was founded by Trump and offered students instruction on real estate investments.

“It’s a small deal, very small,’’ Trump said of the suit, which could force him to take the stand this summer.

Trump specifically railed against the judge in the case, and at one point noted the judge’s Hispanic ethnicity.